Abstract

The theory, fabrication, and performance of monolithic 4 × 4 single-mode fused couplers is reported. The field coupling matrix is derived and used to show that a device having equal coupling between the four fibers may be obtained. The fabrication of such a device is described, and measurements show that the device exhibits excellent coupling uniformity and low excess loss. The wavelength response of a device designed for equal coupling at 1.53 μm is shown between 1.2 and 1.6 μm.

© 1990 Optical Society of America

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References

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  1. J. R. Stern, J. W. Ballance, D. W. Faulkner, S. Hornung, D. B. Payne, “Passive Optical Local Networks for Telephony Applications and Beyond,” Electron. Lett. 23, 1255–1257 (1987).
    [CrossRef]
  2. C. A. Villarruel, C.-C. Wang, R. P. Moeller, W. K. Burns, “Single-Mode Data Buses for Local Area Network Applications,” IEEE/OSA J. Lightwave Technol. LT-3, 472–478 (1985).
    [CrossRef]
  3. A. M. Hill, “One-Sided Rearrangeable Optical Switching Networks,” IEEE/OSA J. Lightwave Technol. LT-4, 785–789 (1986).
    [CrossRef]
  4. M. E. Marhic, “Hierarchic and Combinatorial Star Couplers,” Opt. Lett. 9, 368–370 (1984).
    [CrossRef] [PubMed]
  5. A. R. L. Travis, J. E. Carroll, “A Possible Fused Fiber In-Phase/Quadrature Measuring Multiport,” Electron. Lett. 21, 954–955 (1985).
    [CrossRef]
  6. Z. Xiaopin, S. Liping, Y. Peida, “New Structure of Optical Homodyne Receiver Utilising a 4 × 4 Fiber Directional Coupler,” Electron. Lett. 24, 1212–1213 (1988).
  7. A. W. Snyder, “Coupled Mode Theory for Optical Fibers,” J. Opt. Soc. Am. 62, 1267–1277 (1972).
    [CrossRef]
  8. D. B. Mortimore, “Wavelength-Flattened Fused Couplers,” Electron. Lett. 21, 742–743 (1985).
    [CrossRef]

1988 (1)

Z. Xiaopin, S. Liping, Y. Peida, “New Structure of Optical Homodyne Receiver Utilising a 4 × 4 Fiber Directional Coupler,” Electron. Lett. 24, 1212–1213 (1988).

1987 (1)

J. R. Stern, J. W. Ballance, D. W. Faulkner, S. Hornung, D. B. Payne, “Passive Optical Local Networks for Telephony Applications and Beyond,” Electron. Lett. 23, 1255–1257 (1987).
[CrossRef]

1986 (1)

A. M. Hill, “One-Sided Rearrangeable Optical Switching Networks,” IEEE/OSA J. Lightwave Technol. LT-4, 785–789 (1986).
[CrossRef]

1985 (3)

C. A. Villarruel, C.-C. Wang, R. P. Moeller, W. K. Burns, “Single-Mode Data Buses for Local Area Network Applications,” IEEE/OSA J. Lightwave Technol. LT-3, 472–478 (1985).
[CrossRef]

A. R. L. Travis, J. E. Carroll, “A Possible Fused Fiber In-Phase/Quadrature Measuring Multiport,” Electron. Lett. 21, 954–955 (1985).
[CrossRef]

D. B. Mortimore, “Wavelength-Flattened Fused Couplers,” Electron. Lett. 21, 742–743 (1985).
[CrossRef]

1984 (1)

1972 (1)

Ballance, J. W.

J. R. Stern, J. W. Ballance, D. W. Faulkner, S. Hornung, D. B. Payne, “Passive Optical Local Networks for Telephony Applications and Beyond,” Electron. Lett. 23, 1255–1257 (1987).
[CrossRef]

Burns, W. K.

C. A. Villarruel, C.-C. Wang, R. P. Moeller, W. K. Burns, “Single-Mode Data Buses for Local Area Network Applications,” IEEE/OSA J. Lightwave Technol. LT-3, 472–478 (1985).
[CrossRef]

Carroll, J. E.

A. R. L. Travis, J. E. Carroll, “A Possible Fused Fiber In-Phase/Quadrature Measuring Multiport,” Electron. Lett. 21, 954–955 (1985).
[CrossRef]

Faulkner, D. W.

J. R. Stern, J. W. Ballance, D. W. Faulkner, S. Hornung, D. B. Payne, “Passive Optical Local Networks for Telephony Applications and Beyond,” Electron. Lett. 23, 1255–1257 (1987).
[CrossRef]

Hill, A. M.

A. M. Hill, “One-Sided Rearrangeable Optical Switching Networks,” IEEE/OSA J. Lightwave Technol. LT-4, 785–789 (1986).
[CrossRef]

Hornung, S.

J. R. Stern, J. W. Ballance, D. W. Faulkner, S. Hornung, D. B. Payne, “Passive Optical Local Networks for Telephony Applications and Beyond,” Electron. Lett. 23, 1255–1257 (1987).
[CrossRef]

Liping, S.

Z. Xiaopin, S. Liping, Y. Peida, “New Structure of Optical Homodyne Receiver Utilising a 4 × 4 Fiber Directional Coupler,” Electron. Lett. 24, 1212–1213 (1988).

Marhic, M. E.

Moeller, R. P.

C. A. Villarruel, C.-C. Wang, R. P. Moeller, W. K. Burns, “Single-Mode Data Buses for Local Area Network Applications,” IEEE/OSA J. Lightwave Technol. LT-3, 472–478 (1985).
[CrossRef]

Mortimore, D. B.

D. B. Mortimore, “Wavelength-Flattened Fused Couplers,” Electron. Lett. 21, 742–743 (1985).
[CrossRef]

Payne, D. B.

J. R. Stern, J. W. Ballance, D. W. Faulkner, S. Hornung, D. B. Payne, “Passive Optical Local Networks for Telephony Applications and Beyond,” Electron. Lett. 23, 1255–1257 (1987).
[CrossRef]

Peida, Y.

Z. Xiaopin, S. Liping, Y. Peida, “New Structure of Optical Homodyne Receiver Utilising a 4 × 4 Fiber Directional Coupler,” Electron. Lett. 24, 1212–1213 (1988).

Snyder, A. W.

Stern, J. R.

J. R. Stern, J. W. Ballance, D. W. Faulkner, S. Hornung, D. B. Payne, “Passive Optical Local Networks for Telephony Applications and Beyond,” Electron. Lett. 23, 1255–1257 (1987).
[CrossRef]

Travis, A. R. L.

A. R. L. Travis, J. E. Carroll, “A Possible Fused Fiber In-Phase/Quadrature Measuring Multiport,” Electron. Lett. 21, 954–955 (1985).
[CrossRef]

Villarruel, C. A.

C. A. Villarruel, C.-C. Wang, R. P. Moeller, W. K. Burns, “Single-Mode Data Buses for Local Area Network Applications,” IEEE/OSA J. Lightwave Technol. LT-3, 472–478 (1985).
[CrossRef]

Wang, C.-C.

C. A. Villarruel, C.-C. Wang, R. P. Moeller, W. K. Burns, “Single-Mode Data Buses for Local Area Network Applications,” IEEE/OSA J. Lightwave Technol. LT-3, 472–478 (1985).
[CrossRef]

Xiaopin, Z.

Z. Xiaopin, S. Liping, Y. Peida, “New Structure of Optical Homodyne Receiver Utilising a 4 × 4 Fiber Directional Coupler,” Electron. Lett. 24, 1212–1213 (1988).

Electron. Lett. (4)

J. R. Stern, J. W. Ballance, D. W. Faulkner, S. Hornung, D. B. Payne, “Passive Optical Local Networks for Telephony Applications and Beyond,” Electron. Lett. 23, 1255–1257 (1987).
[CrossRef]

A. R. L. Travis, J. E. Carroll, “A Possible Fused Fiber In-Phase/Quadrature Measuring Multiport,” Electron. Lett. 21, 954–955 (1985).
[CrossRef]

Z. Xiaopin, S. Liping, Y. Peida, “New Structure of Optical Homodyne Receiver Utilising a 4 × 4 Fiber Directional Coupler,” Electron. Lett. 24, 1212–1213 (1988).

D. B. Mortimore, “Wavelength-Flattened Fused Couplers,” Electron. Lett. 21, 742–743 (1985).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (2)

C. A. Villarruel, C.-C. Wang, R. P. Moeller, W. K. Burns, “Single-Mode Data Buses for Local Area Network Applications,” IEEE/OSA J. Lightwave Technol. LT-3, 472–478 (1985).
[CrossRef]

A. M. Hill, “One-Sided Rearrangeable Optical Switching Networks,” IEEE/OSA J. Lightwave Technol. LT-4, 785–789 (1986).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

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Figures (8)

Fig. 1
Fig. 1

Structure of the 4 × 4 coupler showing strong and weak coupling constants.

Fig. 2
Fig. 2

Modes of the four-fiber structure.

Fig. 3
Fig. 3

Power carried by each fiber as a function of propagation distance z. C s = 0.15 mm−1 and C w = 0.

Fig. 4
Fig. 4

Power carried by each fiber as a function of propagation distance z. C s = 0.15 and C w = 0.06 mm−1.

Fig. 5
Fig. 5

Power carried by each fiber at 1.3-μm wavelength as a function of elongation of the coupler during fabrication.

Fig. 6
Fig. 6

Cross section of a coupler around the waist region.

Fig. 7
Fig. 7

Histogram showing percentage coupling between each input and output fiber.

Fig. 8
Fig. 8

Wavelength response of the 4 × 4 coupler between 1.2 and 1.6 μm.

Equations (10)

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d a 1 d z + i β a 1 = - i [ ( a 2 + a 4 ) C s + a 3 C w ] , d a 2 d z + i β a 2 = - i [ ( a 1 + a 3 ) C s + a 4 C w ] , d a 3 d z + i β a 3 = - i [ ( a 2 + a 4 ) C s + a 1 C w ] , d a 4 d z + i β a 4 = - i [ ( a 1 + a 3 ) C s + a 2 C w ] ,
| - λ C s C w C s C s - λ C s C w C w C s - λ C s C s C w C s - λ | = 0.
B 1 = ( 1 1 1 1 ) , B 2 = ( - 1 - 1 1 1 ) , B 3 = ( 1 - 1 - 1 1 ) , B 4 = ( 1 - 1 1 - 1 ) .
A ( z ) = c 1 B 1 exp [ - i ( C w + 2 C s ) z ] + c 2 B 2 exp ( i C w z ) + c 3 B 3 exp ( i C w z ) + c 4 B 4 exp [ - i ( C w - 2 C s ) z ] ,
c 1 = ¼ [ A 1 ( 0 ) + A 2 ( 0 ) + A 3 ( 0 ) + A 4 ( 0 ) ] , c 2 = ¼ [ - A 1 ( 0 ) - A 2 ( 0 ) + A 3 ( 0 ) + A 4 ( 0 ) ] , c 3 = ¼ [ A 1 ( 0 ) - A 2 ( 0 ) - A 3 ( 0 ) + A 4 ( 0 ) ] , c 4 = ¼ [ A 1 ( 0 ) - A 2 ( 0 ) + A 3 ( 0 ) + A 4 ( 0 ) ] .
A ( z ) = ( a b c b b a b c c b a b b c b a ) A ( 0 ) ,
a = [ cos ( C w z ) cos 2 ( C s z ) + i sin ( C w z ) sin 2 ( C s z ) ] , b = - ½ [ sin ( C w z ) sin ( 2 C s z ) + i cos ( C w z ) sin ( 2 C s z ) ] , c = - [ cos ( C w z ) sin 2 ( C s z ) + i sin ( C w z ) cos 2 ( C s z ) ] .
0 z C w ( z ) d z , 0 z C s ( z ) d z ,
tan ( θ 1 ) = tan ( C w z ) tan 2 ( C s z ) , tan ( θ 2 ) = tan ( θ 4 ) = cot ( C w z ) , tan ( θ 3 ) = tan ( C w z ) cot 2 ( C s z ) .
P 1 ( z ) = ¼ [ 1 + 2 cos ( 2 C s z ) cos ( 2 C w z ) + cos 2 ( 2 C s z ) ] P 1 ( 0 ) , P 2 ( z ) = P 4 ( z ) = ¼ P 1 ( 0 ) sin 2 ( 2 C s z ) , P 3 ( z ) = ¼ [ 1 - 2 cos ( 2 C s z ) cos ( 2 C w z ) + cos 2 ( 2 C s z ) ] P 1 ( 0 ) ,

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